The functional form of the accretion rate in Eq. (REF ) is just the same as in the \(\alpha \) -model of accretion disks of Shakura & Sunyaev [1]} for \(r \gg r_0\) . Moreover, the viscosity parameter \(\alpha \)  has the right functional form \(\displaystyle \alpha \propto \frac{\mathrm {v_t}^2}{c_\mathrm {s}^2}\) , which can be envisaged from the physical interpretation of the stress \(\displaystyle \tau _\mathrm {r\phi } \propto \rho \mathrm {v_t}^2\)  and the definition \(\displaystyle \tau _\mathrm {r\phi } \propto \alpha \rho c_\mathrm {s}^2\)  of the parameter \(\alpha \)  [1]}.
